A Framework for Fair Decision-making Over Time with Time-invariant Utilities

TL;DR

This paper introduces a mathematical framework for ensuring fairness over time in decision-making processes involving multiple stakeholders, addressing complexity and symmetry issues to improve solution efficiency.

Contribution

It develops a novel reformulation and relaxation techniques for fairness-over-time decision problems, enabling more effective optimization with branch-and-cut and row-column generation methods.

Findings

Reformulation removes symmetry, improving solver performance.

A relaxation method aids in constructing high-quality approximate solutions.

Framework applicable to various multi-stakeholder, repeated decision scenarios.

Abstract

Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on problems involving multiple stakeholders and a central decision maker. Repetition of the decision-making provides additional opportunities to promote fairness while increasing the complexity from symmetry to finding solutions. This paper presents a general mathematical programming framework for the proposed fairness-over-time (FOT) decision-making problem. The framework includes a natural abstraction of how a stakeholder's acquired utilities can be aggregated over time. In contrast with a natural, descriptive formulation, we demonstrate that if the aggregation function possesses certain basic properties, a strong reformulation can be written to remove symmetry from the problem, making it amenable to branch-and-cut solvers. Finally, we propose a particular relaxation of this reformulation that can assist in the construction of high-quality approximate solutions to the original problem and can be solved using simultaneous row and column generation techniques.